Step-by-step explanation:
Given that,
The length of a ladder, H = 20 feet
The height of the wall, h = 15 ft
We know that,
[tex]\sin\theta=\dfrac{h}{H}[/tex]
h is perpendicular and H is hypotenuse
So,
[tex]\sin\theta=\dfrac{15}{20}\\\\\theta=\sin^{-1}(\dfrac{15}{20})\\\\\theta=48.59^{\circ}[/tex]
Now using Pythagoras theoerm,
[tex]b=\sqrt{H^2-h^2}\\\\b=\sqrt{20^2-15^2}\\\\b=13.2\ ft[/tex]
Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.
Ben asked his 19 classmates whether they were right handed or left-handed. There were five more right handed classmates than left handed classmates. Write a system of equations that can be used to determine how many of Ben’s classmates were right and left handed.
Answer:
left handed = 7 ; right handed = 12
Step-by-step explanation:
r = right handed
l = left handed
r + l = 19
r = l + 5
If we use substitution method we have:
l +5 + l = 19
2 l = 14
l = 7
r = 7 + 5 = 12
Answers:
The system of equations is
[tex]\begin{cases}y = x-5\\x+y = 19\end{cases}[/tex]
where x and y is the number of right-handed and left-handed people respectively.
The system solves to (x,y) = (12,7)
Interpretation:
There are 12 right-handed people and 7 left-handed people in the class.
=========================================================
Explanation:
x = number of right-handed people
y = number of left-handed people
x and y are positive whole numbers.
There are 5 more right-handed people compared to left-handed people, so we can say x = y+5 which is the same as y = x-5. So you could go for either equation. Let's go for the one where y is isolated.
The second equation to form is x+y = 19 because there are 19 people in the class, and you can only be one or the other (left-handed or right-handed but not both). I'm not considering the possibility anyone is ambidextrous though of course that may happen in a realistic setting.
The two equations then form the system
[tex]\begin{cases}y = x-5\\x+y = 19\end{cases}[/tex]
There are a number of ways we can solve this system. Substitution is possibly the quickest way.
x+y = 19
x+(x-5) = 19 ... replace y with x-5; due to the first equation
2x-5 = 19
2x = 19+5
2x = 24
x = 24/2
x = 12 .... this is the number of right-handed people
y = x-5
y = 12-5
y = 7 .... this is the number of left-handed people
The following is a parallelogram solve for the variables
Answer:
x = 13, y = 26, z = 5
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
2x + 110 + 44 = 180
2x + 154 = 180 ( subtract 154 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13
------------------------
2x and y are alternate angles and congruent , so
y = 2x = 2(13) = 26
--------------------------------
The opposite sides of a parallelogram are equal
3z - 1 = 14 ( add 1 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
Earned income and capital gains (or "portfolio income") are acquired in different ways. Which statement describes how they are different?
Answer:
n
Step-by-step explanation:
What is the slope ? Simplify your answer and write it as a proper fraction
the value of ( 7 + 4root 3) ( 7 - 4 root 3) is
Answer:
Step-by-step explanation:
(a + b)(a - b) = a² - b²
[tex](7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1[/tex]
[tex]\boxed{1}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex](7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1[/tex]
You can also use the identity:
( a + b ) ( a - b ) = [tex] {a}^{2} - {b}^{2}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
What is 1/4 as a number?
Answer:
.25
Step-by-step explanation:
you divide 1 by 4 which equals .25
Answer:
1/4 as a number is 0.25
Step-by-step explanation:
Divide 1 by 4 = 0.25
ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is 45.
Question:
ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.
Answer:
101.5cm²
Step-by-step explanation:
The figure for the trapezium ABCD is attached to this response.
To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;
A = [tex]\frac{1}{2}[/tex] x (a + b) x h ------------------(i)
Where;
A = area of the trapezium
a and b are the parallel sides of the trapezium
h = height of the trapezium.
As shown in the figure,
AB and CD are parallel
Therefore, we can say that;
a = AB
b = CD
Also, from the figure,
The height of the trapezium is BP
Therefore, we can say that;
h = BP
We know that;
a = AB = 4cm
b = CD = 25cm
h = BP = 7cm
Substitute these values of a, b and h into equation (i) as follows;
A = [tex]\frac{1}{2}[/tex] x (4 + 25) x 7
A = [tex]\frac{1}{2}[/tex] x (29) x 7
A = 101.5
Therefore, the area of the trapezium is 101.5cm²
Mike drew a quadrilateral with 4 right angles and 2 pairs of opposite sides that are parallel. Name the quadrilateral she could have drawn
Answer:
Rectangle
Step-by-step explanation:
The polygon that contains 4 sides is known as the quadrilateral
Also there are 6 types of quadrilateral that are as follows;
a. The rectangle has 2 pairs of opposite sides & 4 sides of the interior angles
b. The square contains the 4 congruent sides & 4 right interior angles
c. The parallelogram has 2 pairs of opposite sides that are parallel & congruent and 2 pairs of angles that are opposite & congruent
d. The rhombus contains the 4 congruent sides and angles
e. The trapezium contains the one pair of parallel sides
f. The kite contains the two pairs of sides that are congruent adjacent
Al trazar en el plano cartesiano el angulo a cuyo lado terminal es el punto de ( 3,4). Los valores de las funciones del coseno y cocecante son
Answer:
[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]
[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]
Step-by-step explanation:
El cos(α) se define como el cociente entre el cateto adyacente y la hipotenusa.
El valor del cateto adyacente en nuestgro caso es CA = 3.
La hipotenusa se calcual de la siguiente manera:
[tex]h=\sqrt{3^2+4^2}=5[/tex]
Por lo tanto, el cos(α) sera:
[tex]cos(\alpha)=\frac{3}{5}=0.6[/tex]
El cosec(α)=h/CO.
El cateto opuesto CO = 4 y la hipotenusa h = 5
Por lo tanto, el cosec(α) sera:
[tex]cosec(\alpha)=\frac{5}{4}=1.25[/tex]
Espero te haya sido de ayuda!
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4.
y=-6x+
+
Oy-x-6
O y=x+6
O y=6x+
PLEASE I NEED HELP
First, we have to understand the slope-intercept form.
[tex] \large \boxed{y = mx + b}[/tex]
A linear function/equation has three forms and the slope-intercept is one of the form. It is also commonly used in Function topic while the other two forms are commonly used in Analytic Geometry.
In the slope-intercept form, the m-term represents the slope while b-term represents the y-intercept of a graph.
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6.
As you notice the bold, italic and underlined words in the question that I quoted or rewrote. I've just explained that the slope is m-term and y-intercept is b-term.
Therefore, substitute m = 5 and b = -6 in the equation.
[tex] \large{y = mx + b \longrightarrow \bold{y = 5x + ( - 6)}} \\ \large \boxed{ \tt{ \purple{y = 5x - 6}}}[/tex]
I hope this helps! Let me know if you have any questions regarding the linear function, don't hestitate to ask. Good luck with your assignment and have a nice day!
Maria is planning a road trip of 900 miles her car get 30 miles per gallon, and gas cost $3.50 per gallon how much should she budget for the trip
Answer:
Maria should budget $105 for the trip.
Step-by-step explanation:
First divide every 30 miles she is going doing for the trip.
900 divided by 30 = 30
So she will need 30 gallons to drive 900 miles.
30 x 3.50 = 105.
105 is how much she will pay for the gas.
Which of the following are magnitudes for rotational symmetry of the regular octagon below about the marked point?
The magnitude of rotational symmetry of the regular octagon below the marked point is 45°, so option A is correct.
What is octagon?Eight sides, eight internal angles, and eight vertices are the characteristics of an octagon. An octagon is referred to as being regular if all of its sides and angles have the same measurements.
Given:
From the figure, the lengths of the side of the octagon are equal,
So the angle will also be equal,
And we know that octagon has 8 interior angles and their sum is 360 degrees.
Now for measure of one angle = 360° / 8 = 45°,
Therefore, the magnitude of rotational symmetry of the regular octagon below the marked point is 45°.
To know more about octagons:
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why does safari take forever to load ...
Answer:
God knows. But I guess if you have iphone x and after it shouldn't take so long. I have iphone 12 pro max and it works flawlessly.
Answer:
I don't know but I've been thinking the same thing
Giovanna has a score of
−5minus, 5 in Canasta. Vera's score is
Write an inequality that correctly compares the scores.
Answer:'
-9.7 minus, in 13
Step-by-step explanation:
Use 3.14 = 7 to find the volume of the composite shape below.
15 in
20 in
18 in
The total volume of this composite shape is
Awnser: 16022 in3
Step-by-step explanation:
find the volume of the 2 cones find the volume if the semicircle then add the 2 volumes together.
HELP! BRAINLIEST WILL BE GIVEN;/ PLEASE
Answer:
17
Step-by-step explanation:
2(3x+3) = 6x-16+4x-10
6x+6=10x-26
-4x=-32
x=8
6x-16 = 48-16=32
3x+3 = 24+3=27
4x-10= 32-10=22
as arithmetic sequence WZ should be 17
I’m confused a little please help
Answer:
m∠E = 60°
Step-by-step explanation:
The given information in the diagram are;
The shape of the drawing, ΔEDF = A right triangle
The length of the hypotenuse side opposite the right angle = 16·√46
The length of the leg adjacent to the reference angle ∠E = 8·√46
By trigonometric ratio, we have;
[tex]\dfrac{Adjacent\ leg \ length}{Hypotenuse \ length} = cos\angle E[/tex]
Plugging in the values gives;
[tex]cos\angle E = \dfrac{8 \cdot \sqrt{46} }{16\cdot \sqrt{46} } = \dfrac{1}{2}[/tex]
∴ m∠E = arccos(1/2)
Using a calculator or from tables or an online trigonometric ratio tool, we have
arccos(1/2) = 60°
∴ m∠E = arccos(1/2) = 60°.
What's the inverse of f(x) = x-3/5
Answer:
y = x + 3/5
Step-by-step explanation:
1. Label this function 'y': y = x - 3/5
2. Interchange x and y: x = y - 3/5
3. Solve this for y: y = x + 3/5
This last result is the inverse of the given function.
Answer:
y = x + 3/5
Step-by-step explanation:
change f(x) to 'y'
y = x - 3/5
interchange 'x' with 'y'
x = y - 3/5
solve for y
y = x + 3/5
round 0.982 to 2 decimal places
Answer:
0.98
Step-by-step explanation:
0.982,0.98()2 (round up if 5+ down 4-) 0.98
The number 0.982 rounded of to two decimal places will be 0.98.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
The digit 5 acts as a limit.
if the right-sided digit to the digit where we've to round off is < 5, we keep it the same and make all right-sided values 0, and if the right-sided digit is > 5, then we make it increase by 1, and the rest of the right-sided digits become 0. If the digit on right is 5, and after it, there are only zeros or no value, then we round up (increase by 1, as we did in 347500 -> 34800 ) (Well there are many detailed rules of rounding)
Since the given number is 0.982, and in this number the thousandth place is taken by 2, therefore, the number when rounded off will be equal to 0.98.
Hence, the number 0.982 rounded of to two decimal places will be 0.98.
Learn more about Rounding Numbers here:
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What is the factored form of the following expression? 25x^2 + 70x+ 49
Answer:
( 5x + 7 ) ²
Step-by-step explanation:
25 x ² + 70 x + 49
Identity Used
(a + b) ² = a ² + 2 ab + b ²= 25 x ² + 35 x + 35 x + 49
= 5 x ( 5x + 7 ) + 7 ( 5 x + 7)
= ( 5x + 7 )
More to know about Algebraic Identities :-
➛ (a + b)² = a² + 2ab + b²➛ (a - b)² = a² - 2ab + b²➛ a² - b² = (a +b) (a-b)➛ (x + a) (x + b) = x² + (a + b) x + ab➛ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac➛ (a + b)³ = a³ + b³ + 3ab (a + b)➛ (a - b)³ = a³ - b³ - 3ab (a + b)➛ a³ + b³ + c³ = 3abc (If a + b + c = 0)➛ a² + b² + c² = (a + b + c)² - 2 (ab + bc + ca)Answer:
(5x + 7)2.
The expression is in the form a2x2 + 2abx + b2, where a = 5 and b = 7.
Thus, it can be factored as a perfect square trinomial.
If the scale factor of a figure is 6, what is the new length of the enlarged figure matched to the length of the orginal?
Original: 1 cm
Enlarged: 6 cm
Original: 7 cm
Enlarged: 42 cm
Original: 2.5 cm
Enlarged: 15 cm
Original: 5 cm
Enlarged: 30 cm
Answers:
Original = 1 ----> Enlarged = 6Original = 7 ----> Enlarged = 42Original = 2.5 ----> Enlarged = 15Original = 6 ----> Enlarged = 30It looks like you have the correct order. To get those answers above, we simply multiply the original length by the scale factor 6.
Example: 7*6 = 42
convert: 1 hour to seconds
1 min = 60 seconds
1 hour = 60 mins = 60 x 60 = 3600 seconds .
Math help please FAST
Answer:
180
60
40
Step-by-step explanation:
Angles in a triangle add up to equal 90 degrees
Equilateral - has all congruent angles and congruent sides
If a triangle has 3 angles and the angles add up to equal 180 then the measure of one angle in an equilateral = 180 / 3 = 60
Bisect means to split into to equal parts
So if you bisect an 80 degree angles you will have two 40 degree angles. ( Because 80/2 = 40 )
Answer:
40°
Step-by-step explanation:
bisecting an angle gives equal angles equivalent to half the size of the bisected angle for each of them
Help us appreciated:)
Solve 8x - 2y = 12 for y.
O A. y = 4x - 12
O B. y 1-8x+12
O C. y = 8x+6
D. y = 4x - 6
Answer:
D
[tex]8x - 2y = 12 \\ 2y = 8x - 12 \\ y = 4x - 6[/tex]
pls help me on this i don't know what to do
Answer:
[tex]\text{A. The zeroes are 8 and -4, because }y=(x-8)(x+4)[/tex]
Step-by-step explanation:
[tex]x^2-4x-32=0,\\(x-8)(x+4)=0,\\\begin{cases}x-8=0, x=\boxed{8},\\x+4=0, x=\boxed{-4}\end{cases}[/tex]
Find a equation of a line that is parallel to y=5x-21 and passes through the point (3,7).
combine the radicals 9✔x -3✔x
Answer:
6√x
Step-by-step explanation:
Given :-
9√x - 3√x .For combining , take √x as common ,
=> √x ( 9 - 3 )
=> √x * 6
=> 6√x
What is the area of a rectangle with side lengths 25 2 5 feet and 46 4 6 feet? Use the grid to help you.
Answer:
1185 10/30 square feet
Step-by-step explanation:
Area of a rectangle = length * width
Given
Length = 25 2/5 feet
width = 46 4/6
Substitute into the formula;
Area = 25 2/5 * 46 4/6
Area = 127/5 * 280/6
Area = 35,560/30
Area = 1185 10/30
Hence the area of the rectangle is 1185 10/30 square feet
3
The school that Willie goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 12 senior citizen tickets and 5 child tickets for a total of $102. The
school took in $156 on the second day by selling 14 senior citizen tickets and 12 child tickets.
Find the price of a senior citizen ticket.
A $6
B $7
C$10
D $4
Answer: A $6
Step-by-step explanation:
Let x = price per child ticket, y= price per senior ticket.
As per given, we have
5x+12y=102 (i)
12x+14y=156 (ii)
From (i), we have
[tex]x=\dfrac{102-12y}{5}[/tex] (iii)
Put value of x in (ii), we get
[tex]12(\dfrac{102-12y}{5})+14y=156\\\\\\ \dfrac{1224-74y}{5}=156\\\\\\1224-74y=5\times156\\\\\\ 1224-74y=780\\\\\\ 74y=1224-780\\\\\\ 74y=444\\\\ y=\dfrac{444}{74}\\\\\\ y=6[/tex]
Hence, the price of senior ticket = $6
Thus the correct option is A.